This problem, put in a different context, was exactly the same as the previous example
![alt text](/filestore/BlogImage/16641d19-83ee-4437-9956-21a04be10aeb/781c705f-dbcc-4081-ad32-40de04912389TeacherDiaryblogphoto.jpg "Blog image") Our teacher diary follows one maths teacher's journey using LbQ. Duncan Whittaker at St Christopher’s Church of England High School gives us a snapshot of its application and its impact in these regular updates. 7.4 - This class are well-behaved and passionate about improving their maths skills. They are at their happiest when using LbQ and the tablets. They are a confident group of students who are unafraid of asking for help when they need it, whether that be from each other or from me. Their average current estimated grade for the end of year 11 is grade 4. ### 23rd May 2019 Aim of the lesson: to revise percentage questions using [Compare Two Quantities Using Percentages](https://www.lbq.org/search/mathematics/decimals-and-percentages/percentages/compare-two-quantities-using-percentages?years=8&keywords=percentages). Length of session: 32 mins 24 secs Number of students: 24 Number of answers: 556 Answers right first time: 61% ### Learning by Questions lesson overview The previous day, I had planned a feedback lesson for the end of year 7 maths exam. I noticed that the class as a whole dropped several marks on problems involving percentages. I got the impression that the pupils had struggled with the language of the questions as they could do standard percentage questions competently. I needed a resource with lots of different questions that used a wide variety of language - and there are none better than LbQ. This Question Set was originally produced with year 8 pupils in mind and hence it would be a challenge for my year 7 class. I started the lesson using the question, “Dave scored 32 out of 46 in maths and 38 out of 57 in English - which test did he do best in?” I asked the pupils to discuss this problem for 60 seconds then we went through it at the board. Following this, we talked about converting fractions such as ⅖ into a percentage and that the denominator must be 100. Then I ran the Question Set without adapting it. ### Teacher intervention ![alt text](/filestore/BlogImage/16641d19-83ee-4437-9956-21a04be10aeb/fff757e3-1c69-4e18-8ebc-45ec40506dc8Lesson17.JPG "Matrix") **Q4. What is 35 as a percentage out of 28?** Pupil 16 was calculating 28 as a percentage of 35 instead of 35 as a percentage of 28. I explained that my maths test analogy was inappropriate for this question as the maximum you can score out of 28 is 28. The penny had dropped - he had just misinterpreted the language used. **Q5. What is the percentage difference between 8 out of 32 and 34%?** Pupil 23 asked for help with this question. This was the sort of thing I had suspected from the end of year exam - they could do this but just did not understand the language used. I asked, "how do you get 8 out of 32 as a percentage?" Pupil 23 answered correctly straight away. I said, "so what is the difference?" He said, “9%” straight away (which was correct). So he could do this question, but the phrasing had been a barrier. At this point I noticed that Pupil 4 had done very little compared to the others. He said that he had no calculator, so I lent him my own. I told him I expected him to catch up with the others. **Q13. A 0.85 kg tin of chocolates contains 192 grams of fat. What percentage of the chocolates is fat? Give your answer to the nearest whole number.** I paused the lesson so that I could speak to the whole class about this. Initially, I had assumed that the change in units from kg to grams was the main problem. However, I was wrong - they had mostly acknowledged this and knew to convert 0.85kg into grams. They just didn't know what to do from there. ![alt text](/filestore/BlogImage/16641d19-83ee-4437-9956-21a04be10aeb/e9203b08-f919-4457-823a-00c41b5618d0Lesson17example.jpg "Example question") I showed them that the chocolate was analogous to the total in a maths test and that the amount of fat was analogous to the number of marks scored in a maths test. After that, they could do the rest - they just could not see that this problem put in a different context was exactly the same as the maths test example at the start of the lesson. **Q21. Aisha makes 3 glasses of orange. Arrange them in order of strength starting with the glass that contains the greatest percentage of cordial:** **Glass a: 100 ml orange cordial, 300 ml water** **Glass b: 136 ml orange cordial, 410 ml water** **Glass c: 128 ml orange cordial, 380 ml water** I noticed from the matrix that Pupil 14 had got this question wrong 12 times, so I went to help her. I could see that she was finding the concentration of ‘Glass a’ as 100 out of 300. I said, “if you pour 100ml of cordial and 300ml of water into a glass together, how much liquid do you have in total?” She replied, "400 ml." I said, “yes, so your cordial is 100 out of what?” She said, “100 out of 400.” The penny had dropped and it was pleasing to see her answer this correctly. This lesson had provided the pupils with great feedback from their end of year exam and had allowed them to explore a good variety of percentage questions with a significant emphasis on language.